P. D. Srivastava: A Basic Course in Real Analysis (IIT Kharagpur)

# playlist of the 46 videos (click the up-left corner of the video)

source: nptelhrd    2013年7月2日
Mathematics - A Basic Course in Real Analysis by Prof. P. D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Mod-01 Lec-01 Rational Numbers and Rational Cuts 52:37
Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem 54:42
Mod-03 Lec-03 Continuum and Exercises 56:11
Mod-03 Lec-04 Continuum and Exercises (Contd.) 55:00
Mod-04 Lec-05 Cantor's Theory of Irrational Numbers 53:08
Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.) 55:06
Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory 54:37
Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers 55:18
Mod-07 Lec-09 Types of Sets with Examples, Metric Space 55:02
Mod-08 Lec-10 Various properties of open set, closure of a set 55:20
Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set 56:22
Mod-10 Lec-12 Compact Sets and its properties 55:44
Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set 56:08
Mod-12 Lec-14 Tutorial - II 56:13
Mod-13 Lec-15 Concept of limit of a sequence 54:51
Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers 51:48
Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples 54:15
Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem 54:36
Mod-17 Lec-19 Theorems on Convergent and divergent sequences 52:42
Mod-18 Lec-20 Cauchy sequence and its properties 53:53
Mod-19 Lec-21 Infinite series of real numbers 53:16
Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series 54:53
Mod-21 Lec-23 Tests for absolutely convergent series 53:01
Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point 57:20
Mod-23 Lec-25 Some results on limit of functions 53:36
Mod-24 Lec-26 Limit Theorems for functions 54:09
Mod-25 Lec-27 Extension of limit concept (one sided limits) 52:26
Mod-26 Lec-28 Continuity of Functions 54:22
Mod-27 Lec-29 Properties of Continuous Functions 54:07
Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem 56:25
Mod-29 Lec-31 Uniform Continuity and Absolute Continuity 53:41
Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness 55:55
Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness 55:59
Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem 53:52
Mod-33 Lec-35 Mean Value Theorem (Contd.) 56:46
Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule 52:54
Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem 54:06
Mod-36 Lec-38 Tutorial - III 52:42
Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral 53:03
Mod-38 Lec-40 Existence of Reimann Stieltjes Integral 55:39
Mod-39 Lec-41 Properties of Reimann Stieltjes Integral 54:35
Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.) 56:45
Mod-40 Lec-43 Definite and Indefinite Integral 55:39
Mod-41 Lec-44 Fundamental Theorems of Integral Calculus 52:12
Mod-42 Lec-45 Improper Integrals 55:53
Mod-43 Lec-46 Convergence Test for Improper Integrals 53:47

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